Connect with iMac?

There is a wi-fi connection that I have used for my Wii, but I don't know where the base is or who runs it. I don't want to transmit any information like my credit card over that connection.
I was hoping I could use Airport on my iMac to create a connection. I set up a network, and the Wii can find it, but it tells me the password is wrong. Is it possible to use a computer as a connection?

So you don't have internet yourself? You're just mooching off a neighbor? Well, there's not much you can do other than just connect to it. I don't see how you would connect through your computer or what the point would be. Everything will be transmitted through your neighbor's bandwidth regardless of how you set things up on your end.